" 7."(sqrt(5))^(-3)(sqrt(2))^(-3)

(7+3sqrt5)/(7-3sqrt5)=

Simplify each of the following by rationalising the denominator: (7+3sqrt(5))/(7-3sqrt(5)) (ii) (2sqrt(3)-sqrt(5))/(2sqrt(2)+3sqrt(3))

Simplify each of the following by rationalising the denominator: (7+3sqrt(5))/(7-3sqrt(5)) (ii) (2\ sqrt(3)-\ sqrt(5))/(2sqrt(2)+\ 3sqrt(3))

Simplify each of the following by rationalising the denominator,(1)/(5+sqrt(2)) (ii) (5+sqrt(6))/(5-sqrt(6)) (iii) (7+3sqrt(5))/(7-3sqrt(5)) (iv) (2sqrt(3)-sqrt(5))/(2sqrt(2)+3sqrt(3))

Simplify each of the following by rationalising the denominator; 1/(5+sqrt(2)) (ii) (5+sqrt(6))/(5-sqrt(6)) (iii) (7+3sqrt(5))/(7-3sqrt(5)) (iv) (2sqrt(3)-sqrt(5))/(2sqrt(2)+3sqrt(3))

Simplify: (7+3sqrt(5))/(3+sqrt(5))-(7-3sqrt(5))/(3-sqrt(5)) (ii) (1)/(2+sqrt(3))+(2)/(sqrt(5)-sqrt(3))+(1)/(2-sqrt(5))

Factorise : (i) (x-y)^(3)+(y-z)^(3)+(z-x)^(3) (ii) (x-2y)^(3)+(2y-4z)^(3)+(4z-x)^(3) (iv) (3sqrt(2)a-5sqrt(3)b)^(3)+(5sqrt(3)b-7sqrt(5)c)^(3)+(7sqrt(5)c-3sqrt(2)a)^(3) .

Factorise : (i) (x-y)^(3)+(y-z)^(3)+(z-x)^(3) (ii) (x-2y)^(3)+(2y-4z)^(3)+(4z-x)^(3) (iv) (3sqrt(2)a-5sqrt(3)b)^(3)+(5sqrt(3)b-7sqrt(5)c)^(3)+(7sqrt(5)c-3sqrt(2)a)^(3) .

Find the direction cosines of the line which is perpendicular to the lines with direction ratios 4, 1, 3 and 2, -3, 1 . a) (1)/(sqrt(3)),(1)/(5sqrt(3)),(-7)/(5sqrt(3)) b) (5)/(sqrt(3)),(1)/(sqrt(3)),(7)/(5) c) (2)/(sqrt(3)),(5)/(2sqrt(3)),(1)/(7sqrt(3)) d) (1)/(sqrt(3)),(2)/(sqrt(3)),(-1)/(sqrt(3))

Find the value of a and b if (7+3sqrt(5))/(3+sqrt(5))-(7-3sqrt(5))/(3-sqrt(5)) =a + bsqrt(5)